83.24.4 problem 4

Internal problem ID [19318]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (A) at page 81
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:34:03 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }-2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$3)-2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +c_{2} \ln \left (x \right )+c_3 \,x^{3} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,3}]-2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^3}{3}+c_1 \log (x)+c_3 \]